Is 9 the HCF of p and q?

Question

GMATBusters’ Quant Quiz Question -4

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1) LCM of p and q = 75
2) pq = 225

GMATBusters · Answer

Important Concept:

LCM is a multiple of HCF

1) Since 75 is not a multiple of 9, 9 cannot be HCF
Statement 1 is sufficient.

2) pq = 225 
if 9 is HCF the number can be 9a or 9b the product pq = 81ab
since 225 is not a multiple of 81.
Statement 2 is also sufficient.

Answer is D

ashwini2k6jha · Answer

Answer :A
State 1:sufficient
p and q have combination of:5,25 or 1,25
hence hcf of p and q not 15
State 2:not sufficient
pq=225 =3*75 hence HCF=3 HENCE NO
pq=15*15 hence HCF=15 YES

Archit3110 · Answer

Is 15 the HCF of p and q?

1) LCM of p and q = 25
2) pq = 225
#1
1) LCM of p and q = 25
p,q = 25*1 ; 25*5 ;
but HCF wont be 15 ; sufficient 
#2
p*q =225
we know
LCM* HCF = product of any two no
225 = 15*LCM 
LCM= 15 
no info about LCM ; insufficient
OPTION A

uc26 · Answer

1) The highest power of 3 in the LCM is zero. So HCF cannot contain a 3 and thus cannot be 15. Sufficient.
2) We can have different possibilities. 
p=225, q= 1 and the HCF would be 1 and the answer would be NO.
p=15, q=15 and the HCF would be 15 and the answer would be YES.
Not sufficient.

Answer: A

Kinshook · Answer

Asked: Is 15 the HCF of p and q?

1) LCM of p and q = 25
3 is NOT a factor of p or q
15 = 3*5 is not HCF(p,q)
SUFFICIENT

2) pq = 225 
If (p,q) = (1,225); HCF(p,q) = 1
But if (p,q) = (3,75); HCF(p,q) = 3
NOT SUFFICIENT

IMO A

techwave · Answer

Is 15 the HCF of p and q?

1) LCM of p and q = 25
2) pq = 225

ANS: C

1) Statement 1 just proivdes LCM there are many possibilites , hence Not sufficient

2) Pq=225

this will give several values of P and Q . Hence not sufficient.

Combined together. It is sufficinet as we know

product of two numbers = HCF * LCM

225=H*L
H=225/25=9.

MayankSingh · Answer

IMO A

Is 15 the HCF of p and q?

1) LCM of p and q = 25
Let, p= k x a (Where k,a & b are distinct prime number)
q= k x b
LCM = K x a x b
HCF= K
LCM = HCF X (Some Integer)
25 = 15 x (Some integer)
This is not possible for any integer value.

So, 15 not HCF of p & q
Sufficient

2) pq = 225
pq= 3x3x5x5
if p=15 & q=15 , HCF=15
but if =3, q=75, HCF= 3
Not Sufficient

tyson1990 · Answer

Is HCF(p,q) = 15 ?

From ST(1), LCM(p,q) = 25

There could be following cases,
p = 1, q = 25
p = 5, q = 25
p = 25, q = 25

In all cases, HCF(p,q) can never be 15.

Hence, ST(1) is sufficient.

From ST(2), pq = 225
As we know, pq = LCM(p,q) X HCF(p,q)

So, following values can be options 
HCF = 1, LCM = 225
HCF = 5, LCM = 45
HCF = 15, LCM = 15

Hence, ST(2) is not sufficient.

urshi · Answer

Answer - A

This is an easy yet a tricky question. People might me tempted to choose the answer option as C . But pay attention to question. It is a Yes/No question. Hence, we don't need to find a definitive answer.

Statement 1 : LCM of p and q = 25

This implies there is no factor of 3 in p & q. Hence , HCF can't be 15 if there is no factor of 3 in p & q.

SUFFICIENT to say NO

Statement 2 : pq = 225

Case 1 : p*q = 225 = 15 * 15 , in this HCF is 15, Answer is Yes.

Case 2 : p*q = 225 = 5 * 45 , in this case HCF is 5, Answer is No.

So , Statement 2 is insufficient.

Hence, Answer is A.

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AnirudhaS · Answer

(1) LCM of p and q = 25 =  5^2 
Can HCF be = 15 = 3.5? No it cannot, or else the LCM would have at least one factor of 3.
Sufficient

(2) pq = 225 =  3^2. 5^2 
So yes here the HCF may or may not be 15.
**It would be 15 only when both p and q are 15
Not sufficient

IMO  A

firas92 · Answer

GMATBusters

It seems to me that there is a discrepancy between the statements

St.1 - (p,q) can be (1,25) (5,25) or vice versa or (25,25) only

In none of these cases can pq be 225 as given in st.2

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Archit3110 · Answer

GMATBusters 
the initial question posted was Is 15 the HCF of p and q?
1) LCM of p and q = 25
2) pq = 225

everyone here has solved the same aforementioned question but here the question being shown is 
Is 9 the HCF of p and q?

1) LCM of p and q = 75
2) pq = 225

GMATBusters · Answer

yes I realized that there was a contradiction in St1 & 2 as pointed out. so it was revised. Learning never stops... Isn't it

Aks111 · Answer

The question becomes simple if below important property is noted:
  The HCF of a group of numbers is always a factor of their LCM. 
This is true precisely because:
1. HCF is the product of all common prime factors using the least power of each common prime factor 
2. LCM is the product of highest powers of all prime factors.

Statement 1: LCM of two numbers is 75. Since, 9 is not a factor of 75 (3x5x5), 9 cannot be HCF of the two numbers. (Possible HCF's could be: 3, 5, 15, 25, 75)  Sufficient 
Statement 2: HCF should be factor of Product of two numbers. 9(3x3) is factor of 225 (3x3x5x5). But so are 15 (e.g. for p=15 , q=15), 25, 45, 75.. 
Also, for HCF to be 9, the product of numbers should be divisible by 9 twice i.e. 81. Once as factor of p and then as factor of q. Since, 225 is not divisible by 81.
 Sufficient

Fdambro294 · Answer

Key concept (and great question):

The LCM of any set of numbers will provide you with every unique Prime Factor that exists among the set of numbers. However, it will not provide you with the unique breakdown of each number (all we know for sure is that no number can have a prime factor raised to a higher exponent than that contained in the LCM)

In order for P and Q to have a GCF of 9, each number must have (3)^2 included among its prime factorization.

(1) LCM (p ; q) = 75 = (3) (5)^2

If either P or Q had 9 as a factor, then it would NOT evenly divide into the LCM ——> and each number in the set, by definition of the LCM being a multiple of every number in the set, must divide evenly into the LCM

So we have a definite NO because any number that is divisible by 9 can never divide into 75. Therefore, P and Q can NOT share a common factor of 9.

Another way to look at it is that the LCM of a set of numbers always consist of: (GCF) * (remaining coprime factors that remain in each number)

Assuming the GCF of P and Q were = 9

Then:

P = 9(a) ——— and ———- Q = 9(b)

Where a and b are COPRIME Integers - because P and Q have no more common factors

The LCM in this case would be:

LCM = (GCF) * (a * b)

LCM = (9) * (a * b)

Since 225 is not divisible by 9, the GCF of p and q can NOT be 9

S1 sufficient

S2: p * q = 225

When we multiply P and Q, we are essentially “combining” all the prime factors of each number into one larger number.

Therefore, in order for P and Q to share a common factor of 9, at the very least the product of the 2 integers must be divisible by:

P * Q = (9a) (9b) = 81 (a) (b)

Since 225 is not divisible by 81, it is impossible for P and Q to share a GCF of 9

S2 sufficient

D

Great “c trap” laid down

Great question  GMATBusters

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Is 9 the HCF of p and q?

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Is 9 the HCF of p and q?

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